なお，2009 年 3 月以前に判明していた誤りは，増刷にともなって逐次訂正されていますので，2013 年 6 月 24 日に削除しました。なお，ページに (*)がついている項目は，2013 年 6 月以降に追加されたものです。
| ページ |
行 |
誤 |
正 |
22 |
11-12 |
\(\displaystyle + \) |
\(\displaystyle \pm \) |
26 |
↑9 |
行末の \(\displaystyle \lim_{n \to \infty} \frac{1}{n!} = 0\) |
\(\displaystyle \lim_{n \to \infty} \frac{a^n}{n!} = 0\) |
32 |
↑1 |
\(\displaystyle (0 < x < \infty) \) の値域は \(\displaystyle (1,∞) \) |
\(\displaystyle (0 \leq x < \infty) \) の値域は \(\displaystyle [1,∞) \) |
33 |
1 |
\(\displaystyle e^x>1\) |
\(\displaystyle e^x \geq 1\) |
(*) 58 |
11-12 |
\(\displaystyle f'(x) \geq 0 \;\; (0 < x) \) より |
\(\displaystyle f'(x) > 0\;\; (0 < x < 2 \pi) \) かつ \(\displaystyle f'(x) \geq 0 \;\;(2 \pi \leq x) \) より |
(*) 58 |
14 |
\(\displaystyle f(0)=0, \;\; f'(0)=0 \) より |
\(\displaystyle f(0)=0 \) より |
67 |
1 |
定理 3.25，定理 3.26 で， |
定理 3.28，定理 3.29 で， |
75 |
4 |
\(\displaystyle f(x)-f(0) = f'(\theta x) \) |
\(\displaystyle f(x)-f(0) = f'(\theta x) x \) |
75 |
5 |
\(\displaystyle f'(x)=0 \) |
\(\displaystyle f'(\theta x)=0 \) |
75 |
7 |
\(\displaystyle f''(x)=0 \) |
\(\displaystyle f''(\theta x)=0 \) |
75 |
10 |
\(\displaystyle f^{(3)}(x)=0 \) |
\(\displaystyle f^{(3)}(\theta x)=0 \) |
77 |
8 |
\(\displaystyle \sum_{k=0}^n {}_nC_k \, g^{(k)}(x) f^{(n-k+1)}(x) \) |
\(\displaystyle \sum_{k=0}^n {}_nC_k \, h^{(k)}(x) f^{(n-k+1)}(x) \) |
78 |
15-16 |
\(\displaystyle +2n(n+1)P_n(x)=0 \) |
\(\displaystyle -2n(n+1)P_n(x)=0 \) |
(*) 79 |
↑3 |
\(\displaystyle f^{(3)}(x) = - \cos x + 1(\geq 0), \;\; f''(0) = 0 \) より， |
\(\displaystyle f^{(3)}(x) = - \cos x + 1 \)．ここで \(\displaystyle 0 < x < 2 \pi \) のとき \(\displaystyle f^{(3)}(x) > 0 \)，かつ，\(\displaystyle 2 \pi \leq x \) のとき \(\displaystyle f^{(3)}(x) \geq 0 \) であり，\(\displaystyle f''(0) = 0 \) だから， |
(*) 80 |
7 |
\(\displaystyle f''(x)=-\cos x +1(\geq 0). \) |
\(\displaystyle f''(x)=-\cos x +1 \) ．ここで \(\displaystyle f''(x)>0 \;\; (0 < |x| < 2 \pi ) \) かつ
\(\displaystyle f''(x) \geq 0 \;\; (|x| \geq 2 \pi ) \) であり， |
82 |
↑1 |
\(\displaystyle f( \frac{5 \pi}{4} )>0 \) |
\(\displaystyle f''( \frac{5 \pi}{4} )>0 \) |
83 |
1 |
.... 極小値 .... 極大値 ←［極大と極小が逆］ |
.... 極大値 .... 極小値 |
102 |
3 |
\(\displaystyle A+\sqrt{2}B+C-\sqrt{D}=0 \) |
\(\displaystyle A+\sqrt{2}B+C-\sqrt{2}D=0 \) |
107 |
↑8 |
\(\displaystyle I_n=\int \cos^{n-2} x (1-\sin ^2 x) dx = \int \cos^{n-2} dx - \int \cos^{n-2} x \sin^2 x dx = \) |
\(\displaystyle I_n=\int \cos^{n-2} x (1-\sin ^2 x) dx = \int \cos^{n-2}x dx - \int \cos^{n-2} x \sin^2 x dx = \) |
139 |
9 |
\(\displaystyle \lim_{x \to +0} \frac{\frac{-1}{x}}{\frac{-1}{x^2}} - 0 = 0. \) |
\(\displaystyle \lim_{x \to +0} \frac{\frac{1}{x}}{\frac{-1}{x^2}} - 0 = 0. \) |
156 |
↑7 |
行末 |
行末の「-」の前に「)」を追加 |
| 168 |
3 |
\(\displaystyle f_y=3x-3y^3 \) |
\(\displaystyle f_y=3x-3y^2 \) |
190 |
10 |
\(\displaystyle \int\!\!\!\int_\Omega dx dy dz = \int\!\!\!\int_D r^2 \sin \theta dr d \theta d \varphi \) |
\(\displaystyle \int\!\!\!\int\!\!\!\int_\Omega dx dy dz = \int\!\!\!\int\!\!\!\int_D r^2 \sin \theta dr d \theta d \varphi \) |
216 |
2 |
\(\displaystyle \frac{1}{\sqrt{1-u^2}} \frac{dy}{dx} = \frac{1}{x} \) |
\(\displaystyle \frac{1}{\sqrt{1-u^2}} \frac{du}{dx} = \frac{1}{x} \) |
220 |
↑5 |
(2) に条件を追加 |
\(\displaystyle (x>0) \) |
220 |
↑4 |
(4) に条件を追加 |
\(\displaystyle (x>-2) \) |
220 |
↑3 |
(5) に条件を追加 |
\(\displaystyle (-\frac{\pi}{2} < x < \frac{\pi}{2} ) \) |
232 |
6 |
\(\displaystyle y''-4ty'+4y=0 \) |
\(\displaystyle y''-4y'+4y=0 \) |
|
232 |
10 |
\(\displaystyle y''-3ty'+2y=0 \) |
\(\displaystyle y''-3y'+2y=0 \) |
239 |
↑5 |
行中の \(\displaystyle \frac{1}{3} \) |
すべて \(\displaystyle \frac{-9}{5} \) に変更 |